Technical Field
[0001] The invention relates to a method for determining the thickness of one or more layers
of a sample stack of layers or other properties influencing the intensity of light
reflected by the sample stack with an assembly comprising a light source for illuminating
the sample stack of layers and a camera with a detector for detecting the intensity
of light reflected by the sample stack of layers in defined wavelength ranges, the
method comprising the steps of:
- (a) illuminating the sample stack of layers with light from the light source;
- (b) detecting the intensity of light reflected by the sample stack of layers with
the detector in different wavelength ranges; and
- (c) determining the thickness or other property from the intensity detected by the
detector.
[0002] Furthermore, the invention relates to an inspection assembly for determining the
thickness of one or more layers of a sample stack of layers or other properties influencing
the intensity of light reflected by the sample stack comprising:
- (a) a light source for illuminating the sample stack of layers; and
- (b) a camera with a detector for detecting the intensity of light reflected by the
sample stack of layers in defined, different wavelength ranges; and
- (c) computing means for determining the thickness or other property from the intensity
detected by the detector.
[0003] In different branches of the industry flat products are inspected with optical methods
regarding their properties. In the semiconductor- and solar cell industry these are
amongst others wafers and solar cells. Wafers are discs of semiconductor-, glass-,
sheet- or ceramic materials. Such inspected properties may be the thickness of layers
on the surface of the objects. Other inspected properties may be the material composition
of certain layers formed by mixtures of materials. An example of such a mixture is
Si
1-xGe
x which is used to produce strain in a semiconductor transistor. Layers of different
materials are used, for instance, for the production of electronic semiconductor devices
("chips"). Those stacks may contain up to ten layers depending on the specific technology
used.
[0004] A particular field of interest is the fabrication of special wafers, so called SOI
wafers, used for modem semiconductor devices. Current technology wafers have a double
layer on the top surface. The wafers are composed of a silicon oxide layer and a silicon
layer on top of it. In a modem approach regarding new devices especially with lower
power and/or high performance the two layers have a thickness in the range of several
nanometers. The very small layer thicknesses strongly influence the performance of
the chips produced on the wafers. Their accuracy and lateral homogeneity are, therefore,
very important for the chip manufacturing process and the later device performance.
It is, hence, of particular interest to measure the thickness of a layer and its homogeneity
during the manufacturing process with high lateral resolution, high accuracy and within
in a short time per wafer.
[0005] Similar requirements must be fulfilled in other fields. The thickness and lateral
homogeneity of layer stacks may be of crucial importance for end product parameters.
Prior art
[0006] Ellipsometric measurements for nondestructive layer analysis are known in the art.
A sample is illuminated with polarized light. The light is reflected at the interfaces
between the layers or transmitted by the layers and finally detected. The properties
of the layers are determined by the change of the polarization state of the detected
light. Such measured values depend very much on the focus position and the inclination
of the surface of the sample. The method is highly accurate and can be adapted to
very complex layer stacks with many layers involved if an appropriate layer model
is used. Such a method is, however, time consuming requiring several seconds per point
and its spatial resolution is restricted to a few tens of µm. Hence, ellipsometric
measurements are limited in the field of production control.
[0007] A similar consideration applies to the method of spectral reflectometry. Spectral
reflectometry can be performed either by the use of spectrometers or with so called
hyperspectral imaging cameras. Spectrometers provide spectral reflectance data in
several hundreds to thousands of wavelength points. Hyperspectral imaging cameras
provide reflectance data in the range of about 12 to about 256 wavelength points.
Both methods can be used for a quite broad range of thickness values and provide accurate
results. The obtained results strongly depend on the number of wavelength data points
used, but are much too slow for a high speed and high resolution mapping.
[0008] Patent publications
WO2014072109,
EP2426717,
US2014293295, and
US2013063733 disclose the determination of the thickness of one layer (film) of a double layer
stack only using the measurement of the intensity of the reflected light. The disclosed
methods are useful for a measurement where the nominal thickness of both layers is
known and only small deviations from such nominal thickness values shall be determined.
The key idea in all three publications is to restrict the measurement to a small wavelength
range selected in such a way that the influence of the second layer is minimal. The
deviation of the intensity of the reflected light versus thickness variation is nearly
zero within the selected small wavelength range. This idea is based on the fact, that
the intensity of the light reflected by a two layer stack on top of a substrate varies
strongly with the wavelength range due to the interference of the optical waves in
dependence of the thicknesses of the layers.
[0009] The described methods differ in terms of how to get a good reference for the calibration
of the method and which is the best way to avoid influences from the second layer.
The methods can be used either for the top or the bottom layer within the inspected
double layer stack selecting different appropriate small wavelength ranges. However,
all methods mentioned above lack on the fact that they assume that the influence of
the second layer thickness variation is neglectable within the selected wavelength
range. In reality however, it may not be neglected and for a high resolution method
the influence of the second layer can be as high as several percent, rendering the
measured result to be useless.
[0010] Patent application
EP15178999 (not published) by the applicant discloses a method to determine the thickness of
both layers of a double layer system, such as a SOI wafer. This is achieved by measuring
the reflectance of the layer stack in two appropriate wavelength ranges. The simultaneous
measurement in different wavelength ranges is carried out by using a beamsplitter
to generate two optical paths. The different wavelength ranges are then selected with
two filters. It is also disclosed to use gratings or prisms to select a suitable wavelength
range. The intensity of the light is distributed on the two measurement channels which
compromises the signal-to-noise ratio. The known assembly requires many optical components.
[0011] The general physics of the wave reflection at interfaces between two materials are
described by Fresnel formulas. According to the formulas the dependency of the travelling
speed and field amplitude of electromagnetic waves inside a material and along its
interfaces on the material parameters are well known in the art. The most crucial
problem for a theoretical description of the wave propagation is the accurate knowledge
of the material parameters. An example of such a material parameter is the refraction
index. While the Fresnel formulas accurately describe the propagation across smooth,
ideal material interfaces it may be even more complex to correctly consider the surface
roughness effects. In practical solutions, therefore, calibration procedures are required
to complement first principle physics.
[0012] The refraction index is given as a complex value describing the refraction and the
absorption. The method is summarized, for instance, in
WO2014072109. It is the basic idea of the prior art inspection methods to use the light reflected
by a sample stack within small wavelength ranges where the influence of the second
layer is minimal.
[0013] The influence of the two layers within a small thickness range can be described by
approximated relations. A simple example of the prior art uses a layer stack of two
layers named, for example, A and B. Each of the layers of the two layer stack has
a nominal thickness. A Taylor series at the point of the nominal layer thicknesses
of layer A and B can be used to calculate the reflected light intensity R:
wherein
tA : thickness of layer A
tB : thickness of layer B
tA0 : nominal thickness of layer A
tB0 : nominal thickness of layer B
R :actual reflected light intensity measured at the point where layers A and B have
the thickness values tA and tB.
R0 : reflected light intensity where each layer has the nominal thickness, i.e. tA = tA0 and tB = tB0
and
denote partial derivatives of first or second order, respectively, taken at the point
where the layers A and B have their nominal thickness values
ΔtA denotes the difference ΔtA = tA - tA0;
ΔtB denotes the difference ΔtB = tB - tB0.
[0014] The reflected light intensity R varies over the wavelength due to the interference
of the optical waves in dependence of the thicknesses of the two layers. The selection
of a wavelength range where the influence of one of the layers, for example layer
B, is neglectable as it is necessary in prior art measurements means that a wavelength
range must be found where
is nearly zero while
is not zero. Expressed more exactly
must be much smaller than
If higher orders of derivatives are neglected, since their influence is usually smaller
in a Taylor series, the equation (1) then reads:
[0015] Such a relation can be easily used to determine the layer thickness t
A assuming that t
B has its nominal value t
B = t
B0 and has, therefore, neglectable influence on R. The thickness of layer A can be determined
by using a calibration method for the relation between R and t
A. For the calibration layer stacks are manufactured with t
B = t
B0 and t
A with several thickness values around t
A0. The layer stack samples are then measured by a reference method, e.g. ellipsometry
with high accuracy. A calibration curve
R =
f(
tA) can then be created from the measured intensity values at the measured points. This
method is disclosed in above mentioned
WO2014072109. The method has the disadvantage that layer B is assumed to be exactly at its nominal
value t
B = t
B0 at all points. The influence of the thickness of layer B is entirely neglected. This
neglection causes a systematic error of the determined thickness t
A of layer A, which cannot be resolved within the known methods.
[0016] The same consideration holds vici versa for a determination of layer thickness t
B under the assumption that t
A has its nominal value t
A = t
A0.
Disclosure of the invention
[0017] It is an object of the invention to provide an assembly and a method of the above
mentioned kind which allows an accurate measurement of the thickness of one or more
layers simultaneously with high accuracy, high speed and in the single micron and
sub-micron lateral resolution range. It is a further object of the invention to determine
the thickness of one or more layers in a sample stack in a time and cost efficient
way avoiding extensive spectral evaluation methods like ellipsometry or spectral reflectometry
as commonly used.
[0018] According to the invention this object is achieved with the method of the above mentioned
kind, which is characterized in that:
(d) the detector is an array detector with a plurality of detector elements in lines
and columns;
(e) an image of the sample stack of layers is generated on the detector;
(f) the detector comprises a plurality of sections in the form of parallel stripes,
the stripes detecting the intensity of light reflected by the sample stack of layers
simultaneously;
(g) light of one selected wavelength range only is detected by each of the plurality
of sections of the detector; and
(h) a movement of the image of the sample stack of layers on the detector or of the
parallel stripes is generated in a direction perpendicular to the longitudinal direction
of the parallel stripes such that each point of the inspected sample stack of layers
is detected at least once in each of the different wavelength ranges.
[0019] The object is also achieved with an inspection assembly of the above mentioned kind
which is characterized in that
(d) the detector is an array detector with a plurality of detector elements in lines
and columns;
(e) optical means are provided for generating an image of the sample stack of layers
on the detector;
(f) the detector comprises a plurality of sections in the form of parallel stripes,
the stripes adapted to simultaneously detect the light reflected by the sample stack
of layers;
(g) filter means are provided for transmitting only light of one selected wavelength
range to only one of each of the plurality of sections of the detector or detector
elements adapted to measure light of one selected wavelength range only in each of
the plurality of sections; and
(h) moving means are provided for moving the image of the sample stack of layers on
the detector or of the parallel stripes in a direction perpendicular to the longitudinal
direction of the parallel stripes such that each point of the inspected sample stack
of layers is detectable at least once in each of the different wavelength ranges.
[0020] The stripes on the detector may either be a series of lines or a series of columns.
Such lines or columns may be, in particular, neighboring lines or columns. The achieved
result does not depend on the definition of the stripes in this respect. The stripes
extend from one side of the detector to the opposite side of the detector. Detectors,
where each image point consists of 4 color sensitive detector elements as it is the
case with RGB (red-green-blue)-detectors are not suitable for the present invention.
[0021] The light source preferably has a continuous wavelength spectrum extending over all
wavelength ranges which are used for the inspection. It is not necessary that the
emission spectrum has an even intensity distribution, but it is essential that light
is emitted in or converted to all considered wavelength ranges. Suitable continuum
sources have a spectrum, for example, extending from the near UV to VIS in the range
between 400 nm and 800 nm. Such wavelength range is suitable for the thicknesses commonly
used for layers in the wafer production. Obviously, if the thicknesses vary beyond
what is presently used in this field, the wavelength range may differ. It is, however,
also possible to use more than one light source and combine their light to achieve
sufficient coverage of the considered wavelength ranges. The width of the wavelength
range may be represented by the halfwidth, i.e. the wavelength range with an intensity
larger than half of the maximum intensity value. Such width is selected such, that
the intensity of the light is sufficient to provide a good signal-to-noise ratio but
still small enough to allow good accuracy. A halfwidth of, for example 5 to 20 nm
may be suitable in the above wavelength range.
[0022] An imaging optical set-up with components such as mirrors or lenses is used to generate
an image of the sample stack of layers on the detector array. The optical path may
have intermediate imaging planes, but they are not necessary. The image may be generated
with any suitable imaging ratio to obtain a good signal-to-noise ratio and sufficient
high resolution with an affordable detector.
[0023] A relative movement of the image is generated perpendicular to the longitudinal direction
of the stripes between detection steps, i.e. between taking an image. The relative
movement can be effected in numerous different ways. It is possible to move the carrier
of the sample stack of layers. It is also possible to move the camera with the detector.
Other alternatives only move the image without moving the sample stack of layers or
the camera, by means of, for example, a moveable mirror in the optical path. Another
alternative provides that a filter as described below is moved perpendicular to the
stripes. All alternatives can also be combined. There is only a condition that there
is at least a portion of the movement perpendicular to the longitudinal direction
of the stripes. The movement enables that each detector element detects a different
wavelength range of the same image point.
[0024] The stripes may cover the entire image at one stage. The stripes pass along the image
of the object or vice versa whereby all image points are measured in all wavelength
ranges. The measurements of the entire detector array are used. Only when the filter
is in the range of the edges of the image of the object there will be n-1 measurements
without full use of the detector array, where n is the number of used wavelength ranges.
[0025] Similar to the two-layer stack described above the influence of the layers in a layer
stack with a plurality of layers within a small range of thickness variation can be
described by approximated relations. A simple example uses a layer stack of n layers.
Each of the layers of the n layers in the stack has a nominal thickness t
i0 where i goes from 1 to n. A Taylor series at the point of the nominal layer thicknesses
of all layers can be used to calculate the reflected light intensity R:
wherein:
ti,j : thickness of layer i respectively j
ti0 : nominal thickness of layer i
R : actual reflected light intensity measured at the point where the layers deviate
from their nominal thickness values ti0 by Δti
Ro : reflected light intensity measured at the point where all layers have their nominal
thickness values ti0.
and
denote partial derivatives of first or second order, respectively, taken at the point
where all layers B have their nominal thickness values
Δti denotes the difference Δti = ti - ti0
[0026] The reflected light intensity R detected by the detector element varies over the
wavelength due to the interference of the optical waves in dependence of the thicknesses
of the layers in the stack.
[0027] In order to determine n independent parameters, such as the thickness values for
the n layers, a series of n independent measurements is required. Without restricting
the general idea a film composition variable, such as the composition index in the
Si
1-xGe
x, can be considered in a similar manner as a film thickness. The only difference is
that the partial derivatives in equation (1) is is dThickness/dComposition and not
against a thickness value. In that sense t
i,j above may be also a material composition instead of a thickness value.
[0028] The knowledge of all partial derivatives in equation (1) either from theoretical
calculations or from calibration measurements using reference samples with known thicknesses
and compositions allows determining exactly all n unknown parameters t
i based on the result of n independent measurements. With n measurements equation (1)
represents a set of n independent linear equations for the n derivatives Δt
i which can be solved by common linear equation set algorithms. Such an algorithm may
be, for example, the Gauß-Jordan method.
[0029] In the case that less, such as just one or two unknown parameters representing the
thickness or the material composition shall be determined and for a well restricted
parameter range the result can even be obtained with the measurement at a plurality
of wavelengths without calibration, just based on the theoretical known dependency
of R on the unknown parameters.
[0030] With the present invention it is possible to determine the thicknesses of n layers
in a layer stack accurately. The measurement in n different wavelength ranges requires
the use of n series of calibrating curves. One series for each wavelength range is
needed. Each series provides information about the intensity of the reflected light
under known thickness and composition conditions. If two or more thicknesses shall
be determined, the combination of the thicknesses of the different layers of a stack
belonging to one specific reflectivity is not unambiguous. It is an important feature
of the invention that such a combination can be found by using different wavelength
ranges. The term wavelength range means the range which can be represented by one
single wavelength value, i.e. the range transmitted by an interference filter or the
like and is not meant to extend far beyond several tens of nanometers.
[0031] The intensity of the light reflected by a stack of layers is detected simultaneously
or quasi simultaneously for n wavelength ranges. Thereby, the measurements can be
carried out fast and variations of the set-up will not have any influence. Also, it
turns out to be useful to use normalized values by subtracting dark values and normalizing
the measured intensities by a reference value which is, for example, taken from the
reflection at a well known and stable reference material target.
[0032] In a preferred embodiment of the invention the detector elements in the same section
of the detector are sensitive to one of the different wavelength ranges only. This
means, that a first stripe is sensitive for a first wavelength range and the second
stripe for a different, second wavelength range and so on.
[0033] In an alternative embodiment of the invention the light in the optical path between
the light source and the detector is filtered by a plurality of different bandpass
filters in a striped geometrical order, each bandpass filter transmitting light in
one of the selected wavelength ranges only and positioned in the object plane, the
detector plane, an intermediate image plane or any other plane conjugated to the object.
[0034] A very suitable set-up of the invention uses a high performance scientific camera
with a high dynamic range, high resolution (high pixel count) and high speed. In order
to accomplish the wavelength range set the detector may be combined with a filter
set composed of n bandpass filters. The filter assembly divides the detector area
into n stripes of different sensitivity. It provides n band pass filters to form n
sections in the form of stripes with sensitivities to an individual wavelength range.
After each illumination of the detector and signal acquisition the image is relatively
moved. If, for example, the moving distance is 1/n-th of the overall detector length
in the direction perpendicular to the stripes after n steps the reflectance intensities
in all n wavelength ranges are determined by the detector for the whole field of view
of the camera and stored in a computer. From this information the thickness of the
up to n layers or composition parameters can be calculated using the stored reference
information and/or the calibration curves as described above.
[0035] Selecting specific filters for certain layer combinations can improve the selectivity
of the signal in each wavelength range to a certain layer or layer combination and
improve the signal to noise ratio. This invention provides to use a fixed filter set
and divide the useful sensitivity range of the detector into a series of n wavelength
ranges. With such a set up a wide variety of layer stacks can be measured with sufficient
accuracy. Using a fixed filter set also reduces the complexity of the set-up with
increased stability. This fixed set up may be as well used for a system of less unknown
parameters, e.g. a layer stack of just 2, 3 or 4 layers. In such an application the
additional measurement values provide an over-sampling of the system in terms of measured
quantities and may serve conveniently to improve the robustness of the measurement
by using them within a best fit approach.
[0036] It is known to use wavelength filters in an optical path. Such optical filters, however,
generally have only one wavelength range. In order to avoid imaging of dirt and scratches
on the filter, such known filters are positioned outside of any image planes. Contrary
to such known filters the present invention uses a plurality of wavelength ranges
by, for example, a plurality of wavelength filters. Such filters are positioned in
an image plane. Defects of the filters present in all images will be removed by means
of image processing methods.
[0037] If the filter stripes are provided in an intermediate image plane, it may be useful
to use a filter with two sets of stripes, i.e. two stripes for each wavelength. In
such a way the edges may be measured easily without having to change the moving direction.
[0038] A preferred modification of the invention provides that a series of images are taken
with the detector and a movement of the image of the sample stack of layers on the
detector or a movement of the parallel stripes is generated before each of the images
is taken, the length of the movement corresponding to the width of the sections on
the detector. It is, however, also possible to take more than one image of the sample
stack between the movements. It is preferred to always move the image or filter in
the same direction in order to obtain all information as fast as possible.
[0039] According to a preferred modification of the invention the amount of different wavelength
ranges is identical to the amount of stripes. Thereby, a minimum of transitions between
the stripes is achieved. The stripes all may have the same width.
[0040] According to one alternative of the invention the sample stack of layers has less
layers than wavelength ranges and the thickness and/or other property of at least
one layer is determined from two or more measurements. Each additional measurement
with another wavelength range will improve accuracy or enable better determination
without calibration measurements. In such a case it is possible to determine the thickness
and/or other property of at least one layer from a plurality of measurements without
a measured calibration curve. A plurality of measurements for determining the thickness
and/or other property of only one layer may, however, also be used to improve the
accuracy by fitting the determined values.
[0041] A modification of the invention may provide that the thickness and/or other property
determined without a measured calibration curve is calculated using theoretical values
of material properties of the layers.
[0042] Another alternative modification of the present invention provides that a measured
calibration curve is used for each inspected layer to determine the thickness and/or
other property. Thereby, stacks of up to n layers may be inspected.
[0043] Further modifications of the invention are subject matter of the subclaims. An embodiment
is described below in greater detail with reference to the accompanying drawings.
Brief description of the drawings
[0044]
- Fig.1a
- is a schematic illustration of a device for measuring reflectivity at different wavelengths
simultaneously with a filter set in the detector plane.
- Fig.1b
- is a schematic illustration of a device for measuring reflectivity at different wavelengths
with a moving filter set in an intermediate plane.
- Fig.2
- illustrates the path of the rays in a stack of layers.
- Fig.3
- illustrates an example of the spectral transmission profiles of 6 broadband filters
used in the assembly of Figure 1.
- Fig.4a
- is a schematic view of the broadband filter means used in the assembly of Figure 1.
- Fig.4b
- is a schematic view as in Fig.4a with the moving stack of layers.
- Fig.5
- shows a typical wavelength dependency of the reflection at a multi-layer stack.
- Fig.6
- shows a typical wavelength dependency of the change of reflection at a multi layer
stack.
- Fig.7
- shows a typical calibration curve obtained with ellipsometry.
- Fig.8
- shows a series of calibration curves for several samples of stacks.
- Fig.9
- illustrates the correlation between possible thickness values of two different layers
at different wavelengths.
- Fig.10
- illustrates a typical wavelength dependency of the change of reflection at a two layer
stack for different thicknesses of a SiO2-layer on silicon and different wavelength
ranges which are used for measurements.
Description of the embodiments
1. Embodiment: Measurement of a two-layer stack at 6 different wavelengths.
[0045] Figure 1a and 1b show an assembly 701 to measure the reflectivity of a sample 700
at different wavelength ranges. The sample 700 has a layer stack 702 to be inspected
which is shown by example for a two layer situation in greater detail in Figure 2.
Broadband light 703 from a light source 710, such as an LED, a tungsten lamp or an
arc discharge lamp, is homogenized by optical means 720. The optical means homogenize
the lateral and angular light distribution. This can be achieved by, for example a
glass rod with hexagonal or rectangular cross section or a diffusor. The homogenized
light is then deflected by a 50% mirror 730 through an objective 740 onto the sample
700. This is represented by the schematically illustrated path of light designated
with numeral 704.
[0046] The light is partially reflected at the surface 705 of the sample 700. The intensity
of the reflected light 706 is modulated. The modulation is caused by the interference
effect of light partially reflected at each of the material interfaces as described
below with reference to Figure 2. The light 706 which is reflected back passes the
mirror 730. The light is passing tube optics 780 positioned in front of a detector
800 inside a camera. Thereby, an image of the sample 700 is generated on the detector
800. The detector 800 is a high speed array detector with 2560 x 2160 detector elements.
The detector elements are arranged in lines and columns.
[0047] The filter means 760 is either incorporated here into the detector assembly of the
camera or an intermediate image plane 708 is generated and the filter means is moveably
positioned in the intermediate image plane 708. The filter means 760 serves to filter
the light at desired locations of the sensor chip of the detector by allowing only
certain wavelength ranges to pass. The spectral wavelength selection characteristic
of this embodiment is depicted in Figure 3.
[0048] Figures 4a and 4b show a front view of the filter means 760. Figure 4b also schematically
shows the inspected wafer at two different measuring times time 1 and time 2. The
wafer was moved by moving stage 707 between time 1 and time 2. The filter means 760
consists of 6 parallel stripes 761, 762, 763, 764, 765 and 766 of optical broadband
filters in the wavelength ranges designated with the peak values of the transmission
profile as illustrated in Figure 3, lambda 1, lambda 2...lambda 6. Each of the stripes
extends along the entire width of the detector array, i.e. 2560 detector elements.
The width of the stripes 761, 762, 763, 764, 765 and 766 is one 6th of the width of
the detector array in the same direction, i.e. 360 detector elements. The number of
6 filters is, of course, variable and any number of filter stripes may be used.
[0049] Thereby, the whole active detector array is divided into 6 sections in the form of
parallel stripes extending from one end of the detector to the other. The sections
are used for the 6 different wavelength ranges as illustrated in Figure 3. Each section
on the detector comprises 360 x 2560 detector elements illuminated by each of the
6 wavelength ranges selected by the filter means 760. Hence, at each of these wavelength
areas the light intensity for the particular wavelength interval is determined with
a resolution of 360 x 2560 pixels of the sensor assembly 800.
[0050] The wavelength characteristic of the described embodiment is shown in Figure 3. Six
wavelength ranges are selected in 6 areas of the filter. The figure shows the wavelength
transmission characteristic of each filter. The following table indicates the key
parameters of the filter set up.
FWHM_Mean=20nm |
Filter_1 |
Filter_2 |
Filter_3 |
Filter_4 |
Filter_5 |
Filter_6 |
Filter_7 |
Filter_8 |
Lambda_Pic(nm) |
450 |
484 |
519 |
554 |
590 |
626 |
663 |
700 |
FWHM(nm) |
26 |
23 |
21 |
20 |
19 |
18 |
17 |
16 |
T_Max(%) |
57 |
54 |
52 |
49 |
47 |
44 |
41 |
39 |
T_mean(%)380->800nm |
5 |
5 |
4 |
4 |
3 |
3 |
3 |
4 |
FWHM is the full width at half maximum. Lambda is wavelength of the maximum intensity.
T is the transmission value for the intensity. |
[0051] Using a multi-element sensor assembly as a detector allows measuring the spatial
distribution and homogeneity of the layer thicknesses of the layers very fast. The
calculation described below in greater detail can be performed for each detector element
of the detector assembly separately. One measurement step, thereby, provides a large
number of thickness values of an area or a line of the sample. By adding a movable
station 707 to the assembly 701, which provides a relative lateral movement between
the detector and the sample 700, it is possible to scan the whole sample surface 705
and create a full map of the thickness values of the whole surface 705.
[0052] By using different objectives 740 with different magnification, like it is common
practice for microscopes the lateral resolution of the detector 800 can be adapted
to the needs of the measurement task. Hence, it is possible to measure the thicknesses
of the layers very accurately and with a lateral resolution as low as a few hundred
nanometers with a high speed.
[0053] Figure 2 illustrates the physical effects of the reflection at a sample 700. The
sample 700 is a so-called double layer stack 702. The double layer stack 702 has a
top layer 20 having a refraction index n
1 and a buried bottom layer 30 having a refraction index n
2. The layers 20 and 30 are stacked on a substrate material 40 having the refraction
index n
3. While the substrate is part of the stack its thickness is not an issue regarding
this invention. Therefore, the substrate does not constitute a "layer" as it is meant
here.
[0054] The stack 702 is placed in an environment of ambient material 10, which is air in
the present embodiment. It may, however, be also vacuum, oil or water. The ambient
material 10 has a refraction index n
0. As described above, light 50 is incident on the sample surface 705. The light 50
travels through the ambient material 10. The light is partially reflected at the interface
90 between the ambient material 10 and the top layer 20. Thereby, the light 50 is
split into the initially reflected light 60 and light 70 transmitted through the interface
90 formed by surface 705 while it is refracted at the same time.
[0055] The light is also partially reflected and split into reflected and transmitted light
at each further interface 100 and 110 between the materials 20 and 30, and 30 and
40, respectively.
[0056] All light incident and reflected on any of the interfaces 90, 100 or 110 between
materials 10, 20, 30 or 40 with different refraction indices for multiple times will
finally be reflected into ambient space 10. This is represented by the light beams
80. The intensity measured at the detector 800 of light beams 80 will be smaller intensities
than the intensity of the incident light 50 due to the repeated reflection and transmission
at the interfaces. Since the light 80 is composed of light travelling an additional
way through the layer materials 20 and 30, the waves composing the light 80 are delayed
in time with different time differences with respect to the initially reflected light
60. This causes interference. Thus, the intensity of the measured intensity including
all reflected light 60 and 80 together is modulated by destructive and constructive
interferences of light waves 60 and 80 according to their time delays. Since the time
delays of light 80 are determined by the thickness of the layers 20 and 30 multiplied
by their refraction index n
1 and n
2, respectively, the modulation of the intensity of the reflected light 80 is a function
of the layer thicknesses of layers 20 and 30. Hence, analyzing the intensity modulation
can be used to determine the layer thicknesses of the layers 20 and 30 using the refraction
indices of the materials which are well known.
[0057] The formulas describing this effect are known as Fresnel equations together with
the basic principle of the superposition of electromagnetic waves. The functions may
also be determined by experiments, such as ellipsometry.
[0058] If the intensity is determined as a function of the wavelength of the incident light
50 for, for example, a double layer stack with layers 20 and 30 of known material
on a substrate 40 of known material within an environment of known ambient material
10, a reflection intensity function will be obtained. A typical reflection intensity
function 200 is shown in Figure 5 for a system with a top layer 20 in the form of
a 12 nm silicon layer and a buried layer 30 in the form of a 25 nm silicon oxide layer.
The layers 20 and 30 are stacked on top of a substrate 40 of silicon within air as
ambient material 10. Figure 5 illustrates the effect by example and can be repeated
for any material / thickness combination. The effective reflection coefficient for
the whole ambient / layers / substrate system 200 is shown on the abszissa versus
the wavelength in nm. It can be seen, that light in the range of 400 nm is reflected
with a higher intensity than, for example, light in the range above 500 nm.
[0059] The measured intensity of the reflected light changes if the layer thickness of layer
20 or 30 changes. The change can be expressed mathematically in the form of the partial
derivatives of the reflection divided by the layer thickness.
[0060] Figure 6 shows such ratio for the same wavelength range between 300 nm and 700 nm
as Figure 2. The curves 300 and 310 illustrate the influence of a change of the thickness
of the silicon top layer 20. Curve 310 illustrates such influence with a slightly
different thickness of the oxide layer 30. In the same manner 320 and 330 show the
influence of a change in the thickness of the buried oxide layer 30. Curve 330 represents
a slightly different thickness of the silicon layer 20 compared to the nominal silicon
thickness used for 320.
[0061] The dashed box 340 schematically illustrates a first wavelength range to measure
the thickness of the silicon layer 20. Known methods assume, that due to the nearly
zero value of the derivative of the reflection to oxide thickness as shown by 320
and 330 the influence from the thickness of the oxide layer 30 is much smaller than
the influence of the thickness of the silicon layer and may be therefore ignored.
However, since obviously curves 300 and 310 are not identical in the wavelength range
340 such neglection produces a systematic error.
[0062] The present embodiment, therefore, uses further wavelength intervals 350, 360, 370,
380, 390 for further measurements, which are quasi independent from each other. The
wavelength ranges are defined by the filters shown in Figure 4 with transmission profiles
shown in Figure 3. The thickness layer values will be obtained by using the data from
the independent measurements of the reflection at different wavelength intervals 340,
350, 360, 370, 380, and 390. Since only two layers are inspected with 6 wavelengths
in the present example, there is a certain amount of oversampling. This oversampling
serves to improve accuracy of the results. Up to 6 layers may be inspected with 6
different wavelengths if calibration curves are used. Obviously, any other amount
of layers may also be inspected if a suitable amount of wavelength ranges is selected.
[0063] It is understood, that such calculations can be performed for any number of layers
in the stack. The matrix formalism for the calculation of the layer to layer effect
based on Fresnel equations is well known in the art.
[0064] In order to obtain thickness values from reflectivity measurements a calibration
is carried out. The prior art methods correlate the measured gray value to the "real"
thickness values of the layers. Such "real" values are obtained by, for example, ellipsometry.
It is also possible to use straight forward calculations of the reflected light from
the known material parameters for several thicknesses. In a real embodiment ellipsometry
will, however, provide a good reference method.
[0065] Figure 7 shows a calibration curve 361 according to the prior art for a double layer
system with a 25 nm thick buried bottom oxide layer and various samples having different
silicon layer thicknesses. The reflectivity measurement is made under quasi monochromatic
light conditions using only one small wavelength interval in the wavelength range
340 as illustrated in Figure 6. The reflected intensity is taken for this purpose
as measured intensity normalized against some reflection standard, in order to exclude
apparatus influences. The advantage of the approach using measured values and compare
them with a reference method result is to avoid misinterpretations due to other effects
like e.g. optical effects of the embodiment. The accuracy of the resulting calibration
curve can be further enhanced by deriving the form of the curve from the theory by
calculating the reflection intensity straight forward from known material parameters
and thickness values measured by the reference method and searching for a best fit
to the measured gray values.
[0066] The embodiment of the present invention calibrates by repeating the same procedure
as used for the calibration curve 360 in figure 7 for a series of samples with different
thicknesses of oxide layer 30. Thereby, a series of calibration curves 400, 410, 420,
430, 440, and 450 are obtained which are shown in figure 8. Calibration curve 400,
for example represents the relation between different thicknesses of the silicon layer
30 and the measured intensity for a sample having a thickness of the oxide layer 30
of 23 nm. Calibration curve 410 shows the same with an oxide layer 30 having a thickness
value of 24 nm. Samples with different thicknesses of the oxide layer 30 and with
different thicknesses of the silicon layer 20 are measured. Again, all reflectivity
measurements are carried out at first with light from one small wavelength interval
within the range 340.
[0067] If ellipsometry is used as reference method for the determination of the silicon
thickness, the oxide layer thickness is checked at the same time and the data value
pairs sorted accordingly.
[0068] With such calibration curves, as shown in Figure 8 unknown samples of the same material
system but with unknown layer thicknesses can be inspected by measuring a specific
reflectivity value. For example, if the normalized reflectivity gray level value is
0,3 as illustrated by the straight line 460 in figure 8, the crossing points of the
measured reflectivity in the calibration curves 400, 410, 420, 430, 440, and 450 provide
the relation between possible thickness values of the silicon layer 20 and the oxide
layer 30. The point 470, for example, denotes a first possible combination of a thickness
of the oxide layer 30 of 23 nm and a thickness of the silicon layer 20 of 13.6 nm
(value on ordinate axis) fulfilling the measured reflectivity level at the line 460.
This relation can be established for each calibration curve.
[0069] In other words: the measurement of the reflected intensity of an unknown sample at
one wavelength will provide a plurality of possible thickness combinations which may
be represented by a function. Such a function is represented in the form of curve
500 in figure 7. In order to select the correct values, the measurements are repeated
in a second wavelength interval. In the present embodiment the interval in the wavelength
range 350 (see Fig.4) is used. The result is represented by curve 510 in figure 9.
[0070] A plurality of curves like curves 500 and 510 exist for any of those pluralities
of measurements using different small wavelength intervals of incident light. Any
such pair of curves has just one crossing point 520 where the measured reflection
levels are obtained at the same time from the same two layer thickness values. In
the example of figure 9 this results in a silicon layer thickness of 13.14 nm and
an oxide layer thickness of 24.2 nm.
[0071] Generalizing this approach to m wavelength ranges establishing m measurements and
n unknown parameters where parameters may be layer thicknesses or material compositions
one gets the following consideration. For the m different wavelength ranges, i.e.
quasi-independent measurements, the dependencies of the m reflected intensities in
the m wavelength ranges can be expressed by m surfaces in n+1-dimensional spaces.
The n dimensions are the n parameters, i.e. layer thicknesses or material compositions.
The n+1
st dimension is the intensity in the considered wavelength range. Each of the m wavelength
ranges establishes such an n+1 dimensional space where the surface describes the functional
dependency of the reflected intensity from the n parameters.
[0072] Each of the m measured intensities in the m wavelength ranges now define an n-dimensional
curve on the respective surface describing the possible solution vectors for this
particular intensity value measured. These m curves having n dimensions have at least
one crossing point in common. This crossing point is the final solution vector, characterized
by having the same n parameters and being a point of all m surfaces. Mathematically
this final solution vector is found by solving the equation set of m equations with
m vectors with n vector elements. Of course m, i.e. the number of quasi-independent
measurements, has to be higher or equal than n, the number of unknown parameters like
layer thicknesses or material compositions.
2. Embodiment: Measurement of one SiO2-layer on silicon
[0073] Figure 10 illustrates a different embodiment where the same measurement set-up was
used as described above for the first embodiment. The present embodiment, however,
measures only one layer thickness value which is the thickness of a SiO
2-layer on silicon. The reflection function may be simulated and the simulation can
be adapted to the values by fitting with, for example, a Levenberg-Marquardt-algorithm.
The thicknesses of the layer range from 20 nm to 200 nm. 6 wavelength ranges are used
for the measurements which are designated with numerals 810, 820, 830, 840, 850 and
860. Since 6 values are measured for only one unknown thickness value the statistic
error will be increased. Also, the measuring range is increased: The wavelength range
820 at about 500 nm, would not allow distinguishing between the thickness values 20
nm, 150 nm and 200 nm. With such a measurement alone the result would be ambiguous.
The measurement at several different wavelength ranges will allow distinguishing such
cases.
[0074] In theory there are some restrictions for the measurable parameters. Parameters may
be here any layer characteristic which influences the optical properties of the layer
stack as whole (more exact which influences the refraction index and/or extinction
coefficient). The most prominent examples of such parameters are the individual layer
thicknesses and the material compositions. The set of equations is either unambiguously
solvable and there is exactly one set of parameters. Alternatively, if at least two
of the parameters have an exactly identical effect on the reflection in all n wavelength
ranges or the effects compensate each other, a plurality of solutions may exist. Also,
the method is limited to the range where the Fresnel-equations will not provide another
solution due to its periodic nature. The periodicity of the Fresnel-equations will
limit the method especially to thick layers.
[0075] It is clear, that the given embodiment is only an example to illustrate the method
according to the present invention. Similarly, the method can be used for any other
material and/or thickness combination of a two layer stack on a substrate. Examples
are, among others, strained silicon, silicon-germanium, germanium, gallium-arsenide,
indium-phosphide, indium-arsenide, indium-gallium-arsenide, mercury-telluride, III-V
and II-VI ternary and quaternary semiconductor alloys, other oxides and nitrides,
photo resists, thin metal layers, glass, quartz and plastic materials.
[0076] From the above discussion it is also obvious, that the used wavelength intervals
must not be selected such that the dependency of the reflection from one of the layer
thickness values is minimized. They can be selected more freely e.g. to provide a
high and approximately similar signal level for the reflection measurement to improve
the measurement stability. The wavelength intervals are used to maximize the resolution
of the measurement.
[0077] The present invention does not only enable the determination of the thickness of
a layer but also the determination of the material composition.
1. Method for determining the thickness of one or more layers of a sample stack of layers
(700, 702) or other properties influencing the intensity of light (706) reflected
by the sample stack with an assembly comprising a light source (710) for illuminating
the sample stack of layers (700, 702) and a camera with a detector (800) for detecting
the intensity of light (706) reflected by the sample stack of layers in defined wavelength
ranges (340, 350, 360, 370, 380, 390), the method comprising the steps of:
(a) illuminating the sample stack of layers (700, 702) with light (703, 704, 50) from
the light source (710);
(b) detecting the intensity of light (706) reflected by the sample stack of layers
(700, 702) with the detector (800) in different wavelength ranges (340, 350, 360,
370, 380, 390); and
(c) determining the thickness or other property from the intensity detected by the
detector (800);
characterized in that
(d) the detector (800) is an array detector with a plurality of detector elements
in lines and columns;
(e) an image of the sample stack of layers (700) is generated on the detector (800);
(f) the detector (800) comprises a plurality of sections in the form of parallel stripes
(761, 762, 763, 764, 765, 766), the stripes detecting the intensity of light (706)
reflected by the sample stack of layers (700) simultaneously;
(g) light of one selected wavelength range (340, 350, 360, 370, 380, 390) only is
detected by each of the plurality of sections (761, 762, 763, 764, 765, 766) of the
detector (800); and
(h) a movement of the image of the sample stack of layers (700) on the detector (800)
or of the parallel stripes (761, 762, 763, 764, 765, 766) is generated in a direction
perpendicular to the longitudinal direction of the parallel stripes such that each
point of the inspected sample stack of layers is detected at least once in each of
the different wavelength ranges (340, 350, 360, 370, 380, 390).
2. Method according to claim 1, characterized in that the detector elements in the same section of the detector (800) are sensitive to
one of the different wavelength ranges (340, 350, 360, 370, 380, 390) only.
3. Method according to claim 1, characterized in that the light in the optical path between the light source (710) and the detector (800)
is filtered by a plurality of different bandpass filters (760) in a striped geometrical
order, each bandpass filter (760) transmitting light in one of the selected wavelength
(340, 350, 360, 370, 380, 390) ranges only and positioned in the object plane (705),
the detector plane (800), an intermediate image plane or any other plane conjugated
to the object.
4. Method according to any of the preceding claims, characterized in that a series of images are taken with the detector (800) and a movement of the image
of the sample stack of layers (700) on the detector (800) or a movement of the parallel
stripes (761, 762, 763, 764, 765, 766) is generated before each of the images is taken,
the length of the movement corresponding to the width of the sections on the detector
(800).
5. Method according to any of the preceding claims, characterized in that the amount of different wavelength ranges (340, 350, 360, 370, 380, 390) is identical
to the amount of stripes (761, 762, 763, 764, 765, 766).
6. Method according to any of the preceding claims, characterized in that the sample stack of layers (700) has less layers (20, 30) than wavelength ranges
(340, 350, 360, 370, 380, 390) and the thickness and/or other property of at least
one layer (20, 30) is determined from two or more measurements.
7. Method according to claim 6, characterized in that the thickness and/or other property of at least one layer (20, 30) is determined
from a plurality of measurements without a measured calibration curve.
8. Method according to claim 7, characterized in that the thickness and/or other property determined without a measured calibration curve
is calculated using theoretical values of material properties of the layers (20, 30).
9. Method according to any of claims 1 to 6, characterized in that a measured calibration curve (361) is used for each inspected layer (20, 30) to determine
the thickness and/or other property.
10. Inspection assembly (701) for determining the thickness of one or more layers (20,
30) of a sample stack of layers (700) or other properties influencing the intensity
of light reflected (706) by the sample stack of layers (700) comprising:
(a) a light source (710) for illuminating the sample stack of layers (700); and
(b) a camera with a detector (800) for detecting the intensity of light (706) reflected
by the sample stack of layers in defined, different wavelength ranges (340, 350, 360,
370, 380, 390); and
(c) computing means for determining the thickness or other property from the intensity
detected by the detector (800);
characterized in that
(d) the detector (800) is an array detector with a plurality of detector elements
in lines and columns;
(e) optical means (740, 780) are provided for generating an image of the sample stack
of layers (700) on the detector (800);
(f) the detector (800) comprises a plurality of sections in the form of parallel stripes
(761, 762, 763, 764, 765, 766), the stripes adapted to simultaneously detect the light
(706) reflected by the sample stack of layers (700);
(g) filter means (760) are provided for transmitting only light of one selected wavelength
range (340, 350, 360, 370, 380, 390) to only one of each of the plurality of sections
(761, 762, 763, 764, 765, 766) of the detector (800) or detector elements adapted
to measure light of one selected wavelength range (340, 350, 360, 370, 380, 390) only
in each of the plurality of sections (761, 762, 763, 764, 765, 766); and
(h) moving means (707) are provided for moving the image of the sample stack of layers
(700) on the detector (800) or of the parallel stripes in a direction perpendicular
to the longitudinal direction of the parallel stripes such that each point of the
inspected sample stack of layers (700) is detectable at least once in each of the
different wavelength ranges (340, 350, 360, 370, 380, 390).
11. Inspection assembly (701) according to claim 10, characterized in that the detector elements in the same section of the detector (800) are sensitive to
one of the different wavelength ranges (340, 350, 360, 370, 380, 390) only.
12. Inspection assembly (701) according to claim 10, characterized in that a plurality of different bandpass filters in a striped geometrical order is provided
in the object plane (705), the detector plane, an intermediate image plane or any
other plane conjugated to the object between the light source (710) and the detector
(800), each bandpass filter (760) transmitting light in one of the selected wavelength
ranges (340, 350, 360, 370, 380, 390) only.
13. Inspection assembly (701) according to any of the claims 10 to 12, characterized in that the amount of different wavelength ranges (340, 350, 360, 370, 380, 390) is identical
to the amount of stripes (761, 762, 763, 764, 765, 766).
14. Inspection assembly (701) according to any of the claims 10 to 13, characterized in that the detector (800) is formed by a multi-color line camera with a plurality of wavelength
ranges (340, 350, 360, 370, 380, 390).
15. Inspection assembly (701) according to claim 14, characterized in that the lines of the line camera detector are formed by TDI (time delayed integration)
sensor blocks.